Solving Systems by Graphing and Substitution

Solving Systems by Graphing and Substitution

Open Ended

When is it best to solve a system of equations by graphing?

Open Ended

When is it best to solve a system of equations by substitution?

Poll

Which method of solving would you use for the following system of equations:

y = 3 - x

y = 5 + x

• Graphing

• Substitution

Poll

Which method of solving would you use for the following system of equations:

y = 4

3x + y = 10

• Graphing

• Substitution

Poll

Which method of solving would you use for the following system of equations:

3x + y = 11

y = 5 - x

• Graphing

• Substitution

Multiple Choice

Solve this system of equations by graphing.

y = 4x - 2

y = -x + 3

• (-2,-1)

• (-1,-2)

• (1,2)

• (2,1)

Multiple Choice

Solve the system of equations using substitution:
y = 2x + 5
2x + 2y = 4

• (1, 7)
• (7, 1)
• (2, 9)
• (-1, 3)

Multiple Choice

In 3x + 2y = 10    and    x - 5y = 18, which variable should you isolate first?

• The x in the first equation
• The y in the first equation
• The x in the first equation
• The x in the second equation

Multiple Choice

Solve the system by substitution. 
-5x - 4y = -9
y = 6

• (3, 6)
• (6, -3)
• (-3, 6)
• (6.8, 3)

Multiple Choice

The first step in solving using the substitution method is __________.

• get x by itself
• get y by itself
• get either variable by itself
• add the equations together

Multiple Choice

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

If the solution is infinitely many the lines will ________?

• intersect at exactly one point
• be parallel
• overlap each other
• never exist

Multiple Choice

How many Solutions?

• One Solution
• No solution
• Infinitely Many Solutions
• (0, -1)

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• same lines

Multiple Choice

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph
• Don't touch
• Intersect
• Exist

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)